Approximate controllability of fractional neutral integro-differential inclusions with state-dependent delay in Hilbert spaces

In this paper, we prove the approximate controllability of control systems governed by a class of partial fractional neutral integro-differential inclusions with state-dependent delay in Hilbert spaces. Sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using the fixed-point theorem for discontinuous multi-valued operators due to Dhage with the α-resolvent operator. An example is provided to illustrate the main results.